Proof mass support and sensing system

ABSTRACT

A proof mass support system has a pair of alignment coils for controlling the rest position of an elongate proof mass. The alignment coils are constructed to provide a levitation force when they carry electric currents which varies along the length of the proof mass. The relative strength of the electric currents are tuned in the alignment coils to cause the proof mass to take up a predetermined orientation with respect to one or more degrees of freedom defined by the alignment coils. In an alternative, one or more anti-rotation coils may be arranged to apply a restoring force to the proof mass when electric currents pass therethrough. The proof mass is formed so as to cooperate with the restoring force which acts against rotation of the proof mass away from a predetermined orientation. The system is typically provided as part of a superconducing accelerometer or gravity gradiometer.

FIELD OF THE INVENTION

This invention relates to a proof mass support and sensing system,particularly for use in a superconducting accelerometer or gravitygradiometer.

DESCRIPTION OF THE PRIOR ART

Known superconducting gravity gradiometers (SGGs) make use of theextreme sensitivity of superconducting quantum interference devices(SQUIDs) to measure magnetic flux induced in the device by gravitysignals. The gradiometer incorporates an accelerometer including asuperconducting proof mass and associated support system, whosedisplacement modulates the inductance of a sensing coil. Since themagnetic flux in a closed loop sensing coil circuit must remainconstant, a change in inductance in the sensing coil results in acurrent flowing, which is sensed by SQUID input coils.

U.S. Pat. No. 4,841,772 describes a gradiometer in which the sensing andlevitation coils are mounted on the same side of the proof mass toovercome the effects of a temperature rise.

It is desirable that the gradiometer should reject common-mode signalsbut its ability to do this is dependent upon minimizing alignmenterrors. Conventional proof mass support systems have no means ofminimizing these alignment errors.

SUMMARY OF THE INVENTION

In accordance with the present invention we provide a proof mass supportsystem comprising a pair of alignment coils for controlling the restposition of a proof mass; wherein the alignment coils are constructed toprovide a levitation force, when they carry electric currents, whichvaries along the length of the proof mass; and means for tuning therelative strength of the electric currents in the alignment coils tocause the superconducting proof mass to take up a predeterminedorientation with respect to one or more degrees of freedom defined bythe alignment coils.

It has been found that the proof mass can be sensitively aligned byproviding tunable alignment coils which allow fine adjustment of theposition of the proof mass. This is typically achieved by providingpairs of alignment coils which apply a levitation force with a resultantmoment about the center of mass of the proof mass (i.e. imparting arotational as well as linear acceleration to the proof mass). Typicallyone of the coils applies a clockwise rotational force about a givenaxis, and the other coil provides an anti-clockwise rotational forceabout the same axis. This allows the resultant rotational force of thepair of coils to be controlled by varying their relative strengths.

Typically the system is provided as part of an accelerometer or gravitygradiometer comprising two or more proof masses each having anassociated adjustable support system, whereby alignment errors can besubstantially overcome, ie. the orientation of the proof masses can becontrolled to ensure that each proof mass is substantially collinear orperpendicular with respect to the other.

In the case of an accelerometer comprising a single proof mass only, theadjustable support system according to the invention allows thesensitive axis of the accelerometer to be precisely aligned with respectto the gravitational field.

Typically the proof mass is formed of a superconducting material such asNiobium and is levitated due to the Meissner effect. Alternatively theproof mass may be a non-superconducting conductor, which is levitated byusing eddy currents.

Where the proof mass is superconducting, the alignment coils arepreferably also formed of superconducting material (such as Niobium orNiobium/Titanium), which allows the electric currents to be persistentsuperconducting currents.

Alternatively the alignment coils may be formed of normal metal andcarry ac currents for eddy current levitation.

In the following specification a set of orthogonal x, y and z axes isused and is generally defined in the following way. The alignment coilsprovide a levitation force which varies in the x-direction. Generallythis direction is parallel with the sensitive axis of the proof mass.Typically the proof mass is generally cylindrical and the x-axis liesalong the rotational axis of the cylinder. The y and z axes extendperpendicular to the x-axis and where an external gravity field ispresent (for instance the Earth's Gravity g) the z axis is generallydefined by taking g to point in the negative z direction. These axesdefine the degrees of freedom which are controlled by the alignmentcoils.

Typically the alignment coils comprise elongate coils which extend alongthe length of the proof mass and are constructed such that when theycarry electric current they provide a levitation force which variesalong their length.

In this case the alignment coils typically comprise elongatemeander-pattern coils which extend in a first direction, and provide alevitation force in a second direction perpendicular to the firstdirection which varies along the length of the coil. This means thatrotation about an axis substantially orthogonal to the first and seconddirections is controllable by tuning the relative strength of thecurrents in the pair of coils, each extending in substantially the samedirection and whose levitation force vary along their length in oppositesenses. For instance, the pair of coils may comprise upper z-axisalignment coils (providing a levitation force in the negative zdirection) which extend in the x direction and which provide a variableforce along the x axis which can be varied to rotate the proof massaround the y axis. Typically, the support system will also comprise apair of lower z-axis alignment coils (providing levitation force in thepositive z direction) and an additional two pairs of left and righty-axis alignment coils all of which also extend in the x direction.

The levitation force provided by the elongate alignment coils may bevaried by varying one or both of the distance from the coil to thesurface of the proof mass or the number of turns per unit length of thecoil.

The distance from the coil to the surface of the proof mass may bevaried by winding the coil on the surface of a former having grooveswith a depth which increases along the length of the former.

The number of turns per unit length may be varied by providing meanderpattern coils with a taper which varies along the required direction.

Preferably, the gradiometer further comprises a former having machinedgrooves in which the alignment coils are wound, wherein the depth of thegrooves increases by a constant amount along the former's length. Thevariation in depth produces a cross-over effect between the pair ofalignment coils.

Typically, the alignment coils are wound on a substantially cylindricalformer.

In one example, the alignment coils comprise interleaved sets ofmultiple parallel wires.

By winding the interleaved sets of alignment coils with several parallelwires around a surface of the coil former, the distance between currentreversals can be made larger and the proof mass can be levitatedfurther, the spring constants reduced, the dynamic range increased andthe machining tolerances reduced.

Alternatively, the alignment coils comprise a pair of non-parallel,interleaved coils wound in the grooves.

In another example, the coils may comprise a pair of substantiallyparallel tapered coils.

The alignment coils may be made from any suitable superconductingmaterial such as Niobium, and the former may be made of quartz, macor,sapphire or any other suitable insulator. Alternatively, the alignmentcoils comprise copper coated Niobium or Niobium/Titatium wire wound onand bonded to a copper former.

In an alternative to the alignment coils discussed above (which providea variable levitation force along their length), the pair of coils maybe conventional coils (which will typically provide a substantiallyconstant levitation force along their length) which are displaced withrespect to the center of mass of the proof mass.

The support system typically also comprises sensing coils to detectmovement of the proof mass along the x axis (which in this case is the"sensitive axis" of the accelerometer) which also provide levitationforce in the positive and negative x directions. The x-axis sensingcoils are typically pancake coils which provide a low spring constant asrequired along the sensitive axis.

This full complement of x,y and z sensing and alignment coils allows theproof mass to be levitated in a gravitational field which points in anydirection.

Typically, the proof mass is substantially cylindrical.

In the case of a gravity gradiometer comprising two proof masses,typically each proof mass is provided with one or more differential-modesensing coils and one or more common mode sensing coils. Thedifferential-mode sensing coils are connected to a differential-modesensing circuit which detects differential movement of the two proofmasses. The common-mode sensing coils are connected to a common-modesensing circuit which detects common movement (i.e. in the samedirection). Preferably, the common-mode and differential-mode sensingcircuits are substantially decoupled from each other. This allows thesmall differential signal to be accurately measured independently of thelarge common mode background. Typically, the common-mode sensing circuitincludes passive damping means and the differential-mode sensing circuitincludes active damping means.

Conventional proof mass support systems allow rotation of the proof massabout the sensitive axis, which causes measurement errors.

According to a second aspect of the present invention we provide a proofmass support system comprising at least one proof mass; and a set ofcoils at least one of which is arranged to apply a levitation force tothe proof mass and at least one of which comprises an anti-rotation coilarranged to apply a restoring force to the proof mass when electriccurrents pass through the anti-rotation coil; wherein the proof mass isformed so as to cooperate with the restoring force whereby the restoringforce urges the proof mass towards a predetermined rotationalorientation.

The support system according to the second aspect of the inventionprovides an alternative method of controlling the orientation of theproof mass. The levitation coil or coils providing the levitation forcemay be conventional or may comprise alignment coils according to thefirst aspect of the present invention.

Typically the proof mass is formed of superconducting material withindentations which tend to line up with the anti-rotation coils andadopt a low energy orientation. For instance the anti-rotation coils maycomprise pancake coils which extend in the x direction and line up withgrooves in the proof mass which also extend in the x direction. Thiscauses the proof mass to adopt a low energy orientation whichsubstantially prevents rotation of the proof mass about the x axis.

The anti-rotation force coils may also provide a levitation force inwhich case additional levitation force coils may not be required.

Typically the anti-rotation coils extend along the length of the proofmass and are slightly shorter than the proof mass length. In this waythe geometry produces a negative spring.

Conventional accelerometers or gravity gradiometers having two proofmasses only measure acceleration of each proof mass along a singlesensitive axis.

According to a third aspect of the present invention we provide anaccelerometer or gravity gradiometer comprising first and second proofmasses each having an associated sensing system comprising

(i) a first sensing coil or coils oriented with respect to the proofmass in order to sense acceleration of the proof mass in a firstdirection parallel to the separation of the proof masses;

(ii) a second sensing coil or coils oriented with respect to the proofmass in order to sense acceleration of the proof mass in a seconddirection; and,

(iii) a third sensing coil or coils oriented with respect to the proofmass in order to sense acceleration of the proof mass in a thirddirection.

This allows further acceleration or gravity gradient components to bemeasured.

Typically the second direction is orthogonal to the first direction, andthe third direction is orthogonal to both the first and seconddirections.

Typically the first sensing coil or coils associated with each proofmass are connected to a circuit or circuits which measure lineardifferential and common-mode acceleration of the proof masses along thefirst direction. Typically the second sensing coil or coils associatedwith each proof mass are connected to a circuit or circuits whichmeasure differential and common-mode acceleration of the proof massesalong the second direction. The common-mode signal gives the linearacceleration of the proof masses along the second direction. Thedifferential-mode signal gives the rotational acceleration of the proofmasses about the third axis.

Likewise the third sensing coil or coils associated with each proof massare typically connected to a circuit or circuits which measure thelinear acceleration of the proof mass along the third direction and therotational acceleration about the second direction.

By combining three gravity gradiometers or accelerometers according tothe third aspect of the invention, a tensor gravity gradiometer can beconstructed which measures all components of the gravity gradienttensor.

Typically the second and third sets of sensing coils compriseanti-rotation coils according to the second aspect of the invention.That is, the anti-rotation coils of the two proof masses in agradiometer or two-component accelerometer may be combined as part ofthe sensing circuits for radial linear and angular accelerations.

The following comments relate to systems according to all aspects of thepresent invention.

Preferably, each proof mass has a large surface area to volume ratio andlevitation of the proof mass against gravity occurs in substantially allorientations.

Typically, each proof mass is substantially cylindrical.

In addition to the levitation coils according to the first and secondaspects of the invention, a cantilever spring may also be provided foradditional support to the proof mass.

Typically the proof mass comprises a main body section with one or morerings extending therefrom, and a surface of the or each ring remote fromthe main body section is curved and a coil is located radially outwardlyof the surface of the ring such that, in use, a negative spring isformed. An alternative method of forming a negative spring is to providea set of concave alignment coils which levitate the proof mass andproduce an unstable equilibrium in use such that, in use, a negativespring is formed.

One or more of the three aspects of the invention may be incorporated ina wide variety of accelerometer and gravity gradiometer configurations,including the following:

1) Single proof mass accelerometer.

2) Inline gravity gradiometer (comprising two proof masses with theirsensitive axis collinear).

3) Three-axis gravity gradiometer (comprising three inline gravitygradiometers with their sensitive axis in the three orthogonaldirections).

4) Two-component accelerometer (comprising two proof masses with theirsensitive axes perpendicular to their separation).

5) Cross-component gravity gradiometer (comprising a pair oftwo-component accelerometers oriented orthogonal to each other).

6) Differential accelerometer (accelerometer with two concentric proofmasses with the same sensitive axis and identical centres of mass).

7) Six-axis accelerometer (comprising three linear and three angularaccelerometers).

8) Tensor Gravity Gradiometer (comprising three inline and threecross-component gradiometers).

BRIEF DESCRIPTION OF THE DRAWINGS

An example of a gradiometer in accordance with the present inventionwill now be described with reference to the accompanying drawings, inwhich:

FIG. 1 is an exploded view of part of a gradiometer incorporating aproof mass support system according to the first aspect of the presentinvention;

FIG. 2 is a longitudinal section through part of a gradiometerincorporating a proof mass support system according to the first aspectof the invention;

FIG. 3 is a transverse section along a line A--A in FIG. 2;

FIG. 4 is a more detailed view of part of the section of FIG. 3;

FIG. 5 illustrates general alignment errors in the gradiometer shown inFIG. 3;

FIG. 6 is a section through the part of the gradiometer of FIG. 2 withalignment coils activated;

FIG. 7 illustrates the parameters affecting the coil windings for agradiometer;

FIG. 8 is a plan view of a pair of interleaved windings for a proof masssupport system according to the first aspect of the present invention;

FIG. 9 is a section through the windings of Fig. 8;

FIG. 10 is a plan view of an alternative arrangement for a pair ofinterleaved windings for a proof mass support system according to thefirst aspect of the present invention;

FIG. 11 is a plan view of a tapered winding arrangement for alignmentcoils of a proof mass support system according to the first aspect ofthe invention;

FIG. 12 is a section through the tapered arrangement of FIG. 11;

FIG. 13 shows an example of a former for a proof mass support systemaccording to the first and/or second aspects of the invention;

FIG. 14 is a section through the former of FIG. 13;

FIG. 15 is a section through a gradiometer incorporating a proof masssupport system according to the first and/or second aspects of thepresent invention including its housing;

FIG. 16 is a circuit diagram for the z-axis alignment coils;

FIGS. 17 and 18 are circuit diagrams for x-axis sensing coils;

FIG. 19 is a longitudinal section through a proof mass using curvedlevitation coils which form a negative spring;

FIG. 20 is a longitudinal section through another proof mass using aring shaped coil which forms a negative spring;

FIG. 20A is an enlarged view of part of FIG. 20;

FIG. 21 is a cross-section through a first proof mass support systemaccording to the second aspect of the present invention;

FIG. 22 is a cross-section through an alternative arrangement forrotation prevention according to the second aspect of the presentinvention;

FIG. 23 is a circuit diagram for the z'-axis anti-rotation coilsaccording to the third aspect of the present invention;

FIG. 24 illustrates the configuration of a multi-axis gradiometer;

FIG. 25 illustrates the configuration of a two-component accelerometer;

FIG. 26 illustrates the sensing circuit and proof mass configuration ofa cross-component gravity gradiometer;

FIG. 27 illustrates the configuration of a six-axis accelerometer; and,

FIG. 28 is a cross-section through an alternative proof mass supportsystem according to the first aspect of the present invention.

For purposes of identification, the coils in the following descriptionare variously described as "alignment coils" "sensing coils" and"anti-rotation coils" in order to indicate their primary function.However in some cases these coils may provide additional functions suchas levitation.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 is an exploded view of an accelerometer including a proof masssupport system according to the invention. The accelerometer comprisesan inner former 1 on which are mounted superconducting y- and z-axisalignment coils 42,44 (and 42', 44' on opposite sides not shown) whichextend in the x direction and beyond the edges of a cylindricalsuperconducting Niobium proof mass 3 positioned on the former 1. X-axissensing coils 7,8 are wound on outer formers 34. Further x-axis sensingcoils 5,6 (not shown in FIG. 3) are wound on the outer former 33. Thex-axis coils 5,6,7,8 are typically pancake coils, i.e. substantiallyplanar spirals of wire.

The proof mass shape shown in FIG. 1 (a cylindrical shell main bodysection 100 with a ring or band 101 on the outside) gives a largesurface-to-volume ratio allowing levitation of the proof mass in allorientations against gravity and is a relatively stiff structure for alldegrees of freedom. This configuration also allows sensing of movementin the x-direction, and application of a negative spring (as will beshown later). More than one ring 101 may be provided on the main bodysection, for instance a ring may be provided on each end.

In use the accelerometer is cooled to liquid helium temperature toensure superconductivity.

FIG. 2 is a section through a pair of accelerometers for use in agravity gradiometer. The y- and z-axis alignment coils are omitted forclarity. Respective inner formers 1,2 are provided and proof masses 3,4are positioned radially outwardly of the inner formers. Outer formers33,34 (FIG. 1, not shown in FIG. 2) support x-axis sensing coils, forexample, pancake coils for proof mass 3 L_(c11), L_(d11), L_(c12), andL_(d12), (5,6,7,8 respectively). Likewise, additional outer formers(33', 34' shown in FIG. 15) support x-axis sensing pancake coils forproof mass 4 L_(c21), L_(d21), L_(c22), and L_(d22), (29,30,31,32respectively). The coils shown in FIG. 2 each have four turns. However,more or less turns may be chosen as required for levitation and sensecircuit requirements.

FIG. 3 is a view partially in section along the line A--A in FIG. 2schematically illustrating the relationship of the x-axis sensing coils5,6 and the four pairs of y- and z- axis alignment coils 42,42' and44,44' respectively. The pairs of y- and z-axis alignment coils areindicated generally at 42 (right hand pair of y-coils L_(y11)±), 42'(left hand pair of y-coils L_(y12)±), 44 (upper pair of z-coilsL_(z12)±) and 44' (lower pair of z-coils L_(z11)±). Each pair of coilscomprises a pair of interleaved meander pattern coils (e.g. 21(L_(y12)±) and 22 (L_(y12-)) in the case of the left hand pair ofy-coils 42'). In FIG. 3 there is a general nomenclature for thealignment coils of L₊• and L₋₀, which indicates the direction of slopeof the coils. FIG. 3 is a view taken from the negative x direction. Forexample, a L₋ index is given to indicate that as you travel in thepositive x direction, the y or z-coordinate of the coil decreases withx. Therefore + and - indices do not refer to current flow, but rather tothe direction of slant or taper (see FIGS. 8-12 below). FIG. 4 shows theleft hand pair of y-alignment coils 42' in more detail. As can be seenin FIG. 4, each separate turn of the pair of coils 21 (L_(y12-)) and 22(L₁₂₊) comprises 3 wires (each carrying the same current in use as theother two associated wires).

The wires for coil 21 lie in grooves 19 and the wires for coil 22 lie ingrooves 20 on the outer surface 104 of the former 1. The alternatingdirections of current flow through the turns 21,22 are indicated at 102and 103.

In a conventional single coil gradiometer the proof mass will tend toalign itself parallel to the radial levitation coil. In practice it isnot possible to machine a perfect surface on a proof mass and this willhave an error, such that there is a greater mass towards one end of theproof mass than the other. This mass will be supported by the same forceall the way along and therefore the proof mass will not be horizontal. Amachining error will also make the levitation coil deviate from thehorizontal axis.

In an example of the present invention, the same proof mass-coilconfiguration is provided in three orthogonal directions in a three-axissuperconducting gravity gradiometer (SGG)--see FIG. 24. Referring backto FIGS. 2 and 3, L_(d11) , L_(d12), 6,8 and L_(c11), L_(c12) 5,7 aresuperconducting spiral coils that levitate the proof mass with alevitation force having a low spring constant, and also detect thedifferential and common-mode motions respectively of proof mass 3 alongthe x direction. L_(y12-) (21), L_(y12+) (22) and L_(y11-) (21'),L_(y12+) (22') are superconducting meander-pattern alignment coils (withgeometry to be defined later) that suspend proof mass 1 in they-direction. Similarly, L_(z11+), L_(z11-), 44' L_(z12+), L_(z12-) 44are superconducting meander-pattern alignment coils that suspend proofmass 3 in the z direction. The y- and z-alignment coils are designed toprovide a force with high stiffness (i.e. high spring constant) in theirrespective directions. Corresponding coil arrangements are provided forproof mass 4. When the Earth's gravitational acceleration is in the zdirection, the z-axis coils provide the levitation force againstgravity. In general, when the sensitive x-axis points in an arbitrarydirection with respect to the Earth's gravity, all the coils participatein levitating the proof masses.

The SGG proof masses 3,4 respond to the gravity components along theirrespective sensitive axes and a differential-mode sensing circuit (to bedescribed later) measures the difference between the two resultingdisplacements. If g₁ and g₂ are the gravitational fields (accelerations)at the respective centres of mass of the proof masses 3,4 and n₁ and n₂are the unit vectors along the respective axes (see FIG. 5), the SGGoutput in the absence of platform motions is

    Γ.sub.xx =g.sub.2 ·n.sub.2 -g.sub.1 ·n.sub.1(1)

In an ideal gradiometer, with l representing a baseline unit vector, n₁,n₂ and l are all identical. There are two basic alignment errors whichcan be represented in several equivalent ways. We write:

    n=1/2(n.sub.1 +n.sub.2)                                    (2)

as the average orientation of the gradiometer sensitive axes. The axesparallelism error is δn and the axes collinearity error is given by δl,where ##EQU1##

These misalignments couple linear and angular accelerations of theplatform a and α to the gradiometer and lead to error terms in Γ_(xx)(equation (1)) given by ##EQU2## respectively where l is the baseline ofthe gradiometer. In a practical application of the gradiometer, theseerrors can easily limit the gravity resolution of the instrument.

Consider one of each pair of z-axis alignment coils 44,44' and let thetwo coils be configured in such a way that the levitation force per unitarea, dF/dA, varies along the x-axis in the opposite direction on thetwo opposing coils, as in FIG. 6. If, for example, dF/dA for the topalignment coil 44 increases with x and dF/dA for the bottom alignmentcoil 44' decreases with x, then the stationary position of the proofmass 3 will be tilted up. Further, if there is an acceleration orgravity signal in the x direction, the proof mass 3 will move along itstilted axis 36 because the proof mass will feel an increased upwarddifferential force as it moves forward.

If we now provide a pair of alignment coils on both sides withlevitation forces increasing along x in one pair and decreasing along xin the other pair, we should be able to adjust the alignment of thesensitive axis up or down by a desired amount by adjusting thepersistent currents in the alignment coils. Levitation may be alongeither the z- or the y-axis (or both).

A superconducting meander-pattern coil 110 (shown in FIG. 7) of pitch w(center to center distance between neighbouring turns of wire) at adistance d from the surface 111 of the superconducting proof mass,carrying a current I, exerts a force per unit area on the proof mass:##EQU3## where μ₀ is the permeability of the vacuum. So dF/dA can bevaried either by varying the coil gap d or pitch w, or both, along thesensitive axis. For effective levitation, d should be approximatelyequal to w.

Three specific examples of ways to configure the alignment coils aredescribed below although the invention is not limited to these. Thefirst, (shown in FIGS. 8 and 9), is to have two mutually interleavedmeander-pattern coils, with one 21 slanted up by a small angle δθ andthe other 22 slanted down by the same angle δθ. This corresponds to theconfiguration shown in FIGS. 3 and 4 (except only one wire per turn isshown). If all the current flows in the slanted-up coil 21 and none inthe slanted-down coil 22, the proof mass 3 will be aligned parallel tothe slanted-up coil, with an angle δθ with the x axis. Likewise, if allthe current flows in the slanted-down coil 22 and none in the slanted-upcoil 21, the proof mass will be aligned parallel to the slanted-downcoil, with an angle -δθ with the x axis. For an intermediate currentdistribution, the sensitive axis will lie between these two extremeangles.

The coils can be wound in many different ways and it is possible tochange the distance between current reversals by having each coil,slanted up and slanted down, as several wires in parallel. This isillustrated by the coils 21,22 in FIG. 10 and also in FIG. 4. In eachgroove any number of wires can be placed in parallel. This has theeffect of enabling levitation to greater separations, reducing springconstants and giving a larger dynamic range.

A third configuration (shown in FIGS. 11 and 12) is to have onemeander-pattern coil with an increasing taper 39 interleaved withanother with a decreasing taper 40. If all the current is now stored inthe tapered-up coil 39 and none in the tapered-down coil 40, the proofmass will be tilted up on the right since the turns become more evenlyspaced as x increases, thereby resulting in an effectively larger pitch(w) on the right than on the left. Likewise, if all the current flows inthe tapered-down coil 40 and none in the tapered-up coil 39, the proofmass will be tilted-down on the right. For an intermediate currentdistribution, the sensitive axis will lie between these two extremeangles.

In practice, the proof mass will generally be supported by energizingthe two coils with equal currents. Then final adjustment to make theproof mass horizontal is made by sending a differential current throughthe two coils. By controlling the current in each coil a resultant isproduced such that the proof mass has its optimum alignment.

Quite independently, the second proof mass 4 can be aligned in a similarway so that it is collinear with the first proof mass 3 which is animportant requirement for accurate measurement.

FIGS. 13 and 14 show an example of the coil former 1 for use in thepresent invention. A number of grooves 19,20 are cut into the surface ofthe former longitudinally to receive coil windings, which may be cut bya wire electron discharge machining (EDM) in the case of a metal coilformer.

The former 1 is typically made of sapphire or any suitable insulatingmaterial and has a hollow central portion 35. The wires are insulatedNiobium wires which are positioned in place in the grooves 19,20 on thesapphire former 1 together with a suitable adhesive and bonded in place.

Alternatively the former may be copper, and the wires may be copper cladNiobium or Niobium/Titanium which is directly bonded to the copperformer 1.

A problem which may be encountered with Niobium-Titanium (NbTi) wire isflux creep. To reduce this, multifilament NbTi copper clad wire can beused instead, for example 60 filament NbTi wire of 0.1 mm diameter.

The purpose of bonding the wire to a copper former is to achieve passivedamping of all but the sensitive axis resonance. Alternatively, and moreeasily, these resonances can be damped passively using resistorsexternal to the relevant coils, which then can be mounted on aninsulating former.

FIG. 15 shows a section through a housing of a SGG which incorporatesthe two sets of accelerometers previously described. The housing and asolid support such as a vehicle (not shown) form a platform whosemotions can affect the results obtained from the SGG. The housing iscooled in a liquid helium bath in use. The inner formers 1,2 and outerformers (33,34) and (33',34') are mounted on a Niobium (Nb) inner tube14 and shielded with a Nb outer housing 11. The housing is generallycylindrical surrounding the accelerometers and provided with a cavity 16forming a housing for a SQUID and a cavity 18 for a junction box forelectrical wiring 15. Nb covers 17,19 are provided over the cavities.The superconducting housing surrounding the accelerometers ensures thatthey are not subjected to undue external influences due to electricaland magnetic interference. The housing shields at all frequencies, butis transparent to gravity. Additional external screening is provided bya cryostat (not shown). The levitation coil formers 1,2 can be eithermetallic such as copper or aluminium or an insulator such as macor,quartz or sapphire. The sensing coils are mounted on macor, fused quartzor sapphire coil formers 33,34,33'34'.

Alternative wiring strategies are also possible, particularly one inwhich, referring to FIG. 15, the wiring 15 does not go outside the outercovers 11,19 and the cavities 18 are located entirely within a fullyscreened enclosure.

There are many ways different amounts of currents can be stored invarious alignment coils. One example is given in FIG. 16. All fourz-axis alignment coils 122', 122,121,121' (L_(z11+), L_(z12+), L_(z12-),L_(z11) - respectively), for proof mass 3 are connected together to forma loop in which a persistent current I_(z1) is stored. Likewise, allfour z-axis alignment coils 123', 123,124,124' (L_(z21+), L_(z22+),L_(z22-), L_(z21-) respectively), for proof mass 4 are connectedtogether to form a loop in which a persistent current I_(z2) is stored.

These two superconducting loops are connected in parallel to an inductorL_(z3) and a shunt resistor R_(z3) such that the coils with the sameslant (or taper) always stay on the same branches of the loops. Anothersuperconducting loop containing an inductor L_(z4) and a shunt resistorR_(z4) is coupled through transformers to the two loops sharing L_(z3).

The persistent currents I_(z1) -I_(z4) are stored or changed byinjecting currents from current sources via leads connected to thesuperconducting loops, with heat switch resistors 124,125,126,127activated with currents.

The currents I_(z1) and I_(z2) levitate proof masses 3 and 4 and applystiffness to the z and θ_(y) (rotation about y axis) degrees of freedom.If now a persistent current I_(z3) is stored through the inductor, thiscurrent is divided into four paths containing the alignment coils,weakening the currents through the slanted-up (or tapered-up) coils andstrengthening the currents through the slanted down (or tapered-down)coils. Both proof masses will therefore be slanted down so by selectingthe right sense and adjusting I_(z3), one can reduce δl to anarbitrarily small value and eliminate the sensitivity of the SGG to anangular acceleration about the y axis, α_(y).

If a persistent current I_(z4) is stored in the loop containing L_(z4),this will induce screening currents in the main loops such that thecurrents through the slanted-up (or tapered-up) coils increases and thecurrent through the slanted-down (or tapered down) coils decreases inproof mass 3, slanting-up the proof mass. The current I_(z4) induces anopposite effect on the currents in proof mass 4, slanting down the proofmass. Therefore, by choosing the right sense and adjusting I_(z4) viainput from a second current source by using a heat switch 127, oneshould be able to reduce δn to an arbitrarily small value and eliminatethe SGG sensitivity to a linear acceleration along the z axis, a_(z).

The shunt resistors R_(z3) and R_(z4) are to effect passive damping ofthe angular (α_(y)) and linear (a_(z)) resonant accelerations of theproof masses.

A circuit similar to the one shown in FIG. 16 is also provided for they-axis alignment coils.

Unlike conventional sensing circuits, the differential-mode andcommon-mode sensing circuits for x-axis sensing coils are separated.This allows the improvement that not only is the common-modeacceleration balanced out in the differential-mode circuit, but also thedifferential-mode acceleration is balanced in the common-mode circuit,thus substantially decoupling the two sensing circuits from each other.This then permits passive damping to be used for the common mode, whileactive damping, which is required for the differential mode in order toavoid increasing the thermal Brownian motion noise, is used for thedifferential mode.

The differential-mode sensing circuit is given in FIG. 17. Currents,I_(d1), I_(d2) tune the differential-mode resonance frequency. The ratioI_(d2) /I_(d1) is adjusted to balance out the common mode in thedifferential-mode (Γ_(xx)) SQUID 128 output. I_(d3) is used to achieve awideband common-mode balance.

The common-mode sensing circuit is given in FIG. 18. Currents, I_(c1),I_(c2) tune the common-mode resonance frequency. The ratio I_(c2)/I_(c1) is adjusted to balance out the differential mode in thecommon-mode (a_(x)) SQUID 129 output. R_(c3) (130) is a shunt resistorfor passive damping of the common mode. Because the differential modehas been balanced out from the L_(c3) path that couples to the SQUID,R_(c3) does not damp the differential mode.

Active damping of the differential mode is achieved by the followingmeans. The differential-mode SQUID 128 output Γ_(xx) is narrowbandedaround its resonance and phase-shifted by 90° to produce a damping term.This voltage signal is converted into a current signal i_(d) and is fedback to the inductor L_(c5) of the common-mode sensing circuit. Thiscurrent damps the differential-mode resonance. If desired, aforce-rebalance feedback could also be applied through L_(c5).

In order to have a high gradient sensitivity, the differential-modefrequency must be kept low. On the other hand, the common-mode frequencymust be as high as possible to reduce the common-mode response of theproof masses to platform vibrations as well as to unbalanceddifferential-mode feedback currents. We accomplish this by making L_(c3)small and L_(c4) large compared to sensing coil inductances in thecommon-mode circuit:

    L.sub.c3 <L.sub.c11 ≈L.sub.c12 ≈L.sub.c21 ≈L.sub.c22 <L.sub.c4                              (7)

so that the common and differential modes see an almost short-circuitedor almost open-circuited output inductance, respectively, and by keepingthe differential-mode sensing currents low and the common-mode sensingcurrents high:

    I.sub.d1 ≈I.sub.d2 <I.sub.c1 ≈I.sub.c2     (8)

By providing separate circuits for differential mode and common mode,the differential mode can be balanced in the common mode circuit and thesensitivities of each circuit adjusted independently. Balancing of thedifferential mode in the common mode circuit is not possible in aconventional arrangement where the differential mode and common mode aremeasured from the same set of coils.

The differential-mode and common-mode frequencies can be separatedfurther by applying an additional superconducting negative spring alongthe sensitive axis.

One way of providing a negative spring is by use of curved levitationcoils, as shown in FIG. 19. The concave levitation coils 44A,44A'(similar to 44 and 44') produce an unstable equilibrium for the xposition of the proof mass 3, effectively creating a negative spring inthe x direction.

An alternative configuration is by locating a ring-shapedsuperconducting coil 45 outside the center ring 101 of the proof mass 3whose surface is rounded in this case, as shown in FIG. 20 and at 47 inthe enlarged view in FIG. 20a. A persistent current stored in coil 45produces an unstable equilibrium for the x position of the proof mass 3,providing the desired negative spring. The negative spring can reducethe differential-mode frequency to near zero while maintaining arelatively high frequency for the common mode, thereby improving thesensitivity and common-mode rejection of the SGG.

FIGS. 21 and 22 illustrate first and second embodiments of a proof masssupport system according to the second aspect of the invention.

Rotation of the proof mass about the x axis (θ_(x)) can convert surfaceirregularities of the proof mass into noise in the gradiometer. Theθ_(x) rotation can be stopped by providing two single-turn anti-rotationcoils 48,49 equispaced about the inner circumference of the outer former(not shown), as shown in FIG. 21. Four matching grooves 50 are providedin the proof mass 3. A persistent current stored in the two loops willprovide a restoring force to the proof mass in the θ_(x) direction, thuspreventing an uncontrolled rotation of the proof mass.

An alternative method of rotation prevention is shown in FIG. 22 where,instead of the grooves 50 shown in FIG. 21, cutouts, e.g. in the form ofcircular grooves 55, are made along the entire inner length of the proofmass 3. Pancake anti-rotation coils 51,52,53,54 (L_(z'11), L_(z'12),L_(y'11), L_(y'12)) are wound on the levitation coil former 1. The y'and z' axes are axes rotated by 45° from the y and z axes. The proofmass is then at a minimum energy position when the cutouts 55 areopposite the coils 51-54. These anti-rotation coils have another usefulfunction in stiffening z and y axis motions. If the upper coils 52 and53 are used, they will provide additional levitation with respect togravity (in the negative z direction) and will help bring the coilformer and proof mass closer to concentricity. In a zero-g environment,the anti-rotation coils can become the major stiffening elements for yand z motions if the currents through the meander-pattern alignmentcoils 42,42', 44, 44' are kept small. Small currents through themeander-pattern coils ultimately lead to a very low resonance frequencyfor the sensitive axis.

When the proof masses float symmetrically about the coil former, themeander-pattern coils no longer provide any levitation. Coil L_(z12-)provides levitation which is exactly cancelled by Coil L_(z11-).However, they still provide stiffness and alignment control which is nowtheir main function.

In zero g all the anti-rotation coils will be energised for the purposeof preventing rotation. In the Earth's gravity, only the upper coils 52and 54 need to carry persistent currents.

The anti-rotation coils may be used to sense the radial linear andangular accelerations. FIG. 23 shows a sensing circuit that connects theanti-rotation coils L_(z'11) and L_(z'12) (51,52) of proof mass 3 andthe corresponding coils L_(z'21) and L_(z'22) (56,57) associated withproof mass 4 to sensing SQUIDs 58 and 59. With currents I_(z'1) andI_(z'2) stored in the sense shown, SQUIDs 58,59 measure the linearacceleration along the z' axis (a_(z')) and the angular accelerationabout the y' axis (α_(y')) respectively, where y' and z' are the axesrotated by 45° from the y and z axes. A similar circuit can be providedfor the anti-rotation coils L_(y'11), L_(y'12), L_(y'21) and L_(y'22) tosense the linear acceleration along the y' axis (a_(y')) and the angularaccelerations about the z' axis (α_(z')).

The acceleration components in the y z-coordinates can be obtained fromthe acceleration components measured in the y'z'-coordinates by ##EQU4##

The angular acceleration outputs α_(y) and α_(z) will be integrated toobtain the angular velocities Ω_(y) and Ω_(z) of the platform, whichwill then be used to make the necessary corrections for centrifugalacceleration.

The shunt resistors R_(z'3) and R_(z'4) provide passive damping for theradial translational (a_(z')) and rotational (α_(y')) modes.

The output inductances L_(z'3), L_(z'4) are kept small in comparisonwith the pancake coil (51,52,56,57) inductances to obtain maximumstiffness for both radial translational and rotational degrees offreedom and to prevent overloading the SQUIDs 58 and 59. This may beachieved by adding a small shunt inductance across the SQUID inputcoils.

The anti-rotation coils 51,52,56,57 should not protrude beyond the endsof the proof mass since this would produce a large stray inductance.Therefore the anti-rotation coils are made slightly shorter than thelength of the proof mass. This geometry also has the effect of producinga negative spring.

Since the gradiometer is completely superconducting, it must be storedin a cryostat to cool it to the necessary temperature for operation. Forairborne applications, it is desirable to keep down the size of thedewar, for example, to four foot high by two foot outside diameter.Liquid helium is stored within a mu-metal or cryoperm shield inside avacuum jacket. The vacuum jacket could be formed from Niobium withpenetration welds. If three-dimensional measurements are to be made, thegradiometer requires three-point suspension.

A levitated proof mass gradiometer has a number of advantages. By usinga low resonance frequency, high sensitivity can be achieved. For asignal bandwidth between 10⁻³ and 10⁻¹ Hz, ω_(d) /2π can be maintainedat approximately 0.2 Hz, where ω_(d) is the resonance frequency of thedifferential mode. The displacement at a given frequency is

    x (ω)=a(ω)/(ω.sup.2 -ω.sub.d.sup.2).(11)

The value of ω_(d) /2π achieved is a substantial improvement over agradiometer with a mechanical spring for which ω_(d) /2π is in the range5-10 Hz, thus a proof mass of 0.1 kg may be sufficient in the presentinvention to obtain a gradient sensitivity of 10⁻³ E Hz⁻⁰.5 where 1E=10⁻⁹ s⁻².

A further feature is that the improved alignment results in bettercommon-mode rejection. With a particular arrangement of alignment coils,complete alignment is obtained against both linear and angularaccelerations. While mechanically suspended proof masses have |δn| and|δl| between 10⁻³ and 10⁻⁴, in the present invention |δn| and |δl| canbe reduced to below 10⁻⁶ by adjusting persistent currents I_(y3),I_(y4), I_(z3), I_(z4), in the alignment circuits.

A number of alternative arrangements to the single axis gravitygradiometer discussed above will now be described with reference toFIGS. 24-27. Each of these configurations may incorporate proof masssupport systems according to the first and second aspects of theinvention and/or sensing systems according to the third aspect of thepresent invention.

Three-Axis Gravity Gradiometer

In most circumstances several gradiometers will be used in parallel tomeasure different components of the gravity gradient tensor. Aparticularly useful one is a three axis inline component gradiometermeasuring Γ_(xx), Γ_(yy) and Γ_(zz). One of the major advantages of thisconfiguration is related to the fact that, in free space,

    Γ.sub.xx +Γ.sub.yy +Γ.sub.zz =0          (12)

The sum of the diagonal elements being zero is an extremely useful selfchecking feature for such an instrument which enables the most sensitivemeasurement to be made. It is clear that the single-axis gradiometerdescribed above can be used in a three-axis configuration thereby givingall the benefits that such a configuration confers.

The design looks schematically as shown in FIG. 24. Three inline gravitygradiometers comprising pairs of inline proof masses 230,231,232 arearranged with their sensitive axes in three orthogonal directions(x,y,z). In the Earth's field, the "umbrella" configuration is oftenused whereby all axes make the same angle to the direction of gravity.Each component is then approximately the same, and, as their sum iszero, each will be measuring small signals only.

The SQUID sensing and levitation circuits, alignment coils and negativesprings are all applied in virtually the same way as for the single axisgradiometer described above.

Two Component Accelerometer

A further embodiment of the invention is shown in FIG. 25 which is aschematic diagram of a two-component accelerometer comprising a firstaccelerometer with a proof mass 60, and a second accelerometer with aproof mass 61. Each accelerometer is sensitive to acceleration/gravityin the x direction.

By coupling the SQUID detection circuits in a similar way as shownpreviously for the single axis gradiometer it is possible to measure thedifference in accelerations between the two proof masses across abaseline perpendicular to the sensitive axis. This device measures anangular acceleration in the absence of cross-component gravitygradients.

Using another SQUID circuit it is also clearly possible to measure thelinear acceleration a_(x). Thus this instrument can be configured tomeasure a_(x) and α_(z) (i.e. is a two-component accelerometer). As withthe gravity gradiometer previously described, the arrangement in FIG. 25can also be used to measure all other acceleration components, albeitwith reduced sensitivity.

Cross-Component Gravity Gradiometer

By combining two such two-component accelerometers with their sensitiveaxes orthogonal to one another as shown in FIG. 26, a cross-componentgravity gradiometer can be formed. The gradiometer comprises a firsttwo-component accelerometer comprising a pair of proof masses 170,171,and a second coplanar two-component accelerometer comprising a pair ofproof masses 172,173. With persistent currents stored as shown in FIG.26, SQUIDS 144,145 measure the cross-component gravity gradient Γ_(xy)and the angular acceleration α_(z) respectively.

The sensitive axes can be aligned by using the same procedures as usedfor the gradiometer previously described.

Differential Accelerometer

An extension of the two-component accelerometer is one for which theproof masses have the same sensitive axes and identical centres ofgravity. This forms a differential accelerometer (not shown in anyFigure) and the alignment procedure is identical to that for thesingle-axis SGG.

By forming the two proof masses in the differential accelerometer ofdifferent materials, Einstein's Equivalence Principle can be tested.

Six-Axis Accelerometer

By utilising three of the two-component accelerometers it is possible tomake an instrument which measures all six possible accelerationcomponents, three linear and three angular.

The arrangement would conceptually look similar to the six-axisaccelerometer drawn in FIG. 27. This comprises three two componentaccelerometers 270,271,272 arranged orthogonally.

Tensor Gravity Gradiometer

By utilising the radial sensing circuit shown in FIG. 23 in thethree-axis gradiometer of FIG. 24, or the six-axis accelerometer of FIG.27, a tensor gravity gradiometer which measures all three inline andthree cross-component gravity gradients can be constructed by ensuringmatching of the scale factors of the measurement circuits.

A further alternative embodiment of the y- and z-axis alignment coils isshown in FIG. 28, which is a cross-section showing the z-axis alignmentcoils of a single proof mass support system. In this case the upperz-axis alignment coils 175,176 and lower z-axis alignment coils 177,178are conventional meander-pattern or pancake coils (i.e. they eachprovide a substantially constant levitation force in the x direction).However, since the coils 175-178 are displaced with respect to thecenter of mass of the proof mass 179, their levitation force provides amoment about the y axis. Therefore, by adjusting the relative levitationforces provided by adjacent coils 175,176 and 177,178 the sensitive axisof the proof mass can be aligned with the x axis. If, in the circuitshown in FIG. 16, we use coils 175,178 (shown in FIG. 28) instead of thecoils 122,122' and coils 176,177 instead of 121,121' the alignmentcircuit will work identically. The y-axis alignment coils (not shown)are arranged in a similar way.

Note, by Einstein's Equivalence Principle, all the single proof massaccelerometers just described are also gravimeters, so clearly can beused for sensitive gravimetry.

The proof mass support systems described above all use levitation coilsto levitate superconducting proof masses (due to the Meissner effect)and do not employ any mechanical springs. However, in an alternativeembodiment, part of the levitation force on the proof mass/es may beprovided by cantilever springs.

Typical applications for an accelerometer or gravity gradiometerincorporating a proof mass support system according to the first andsecond aspects of the invention are all areas where ultra sensitivegravimetry, gravity gradient and acceleration measurements are required.

A gravity gradiometer may be used to test that nuclear warheads havebeen decommissioned by comparing gravity gradient with that expected.Low noise reconstruction of the gravity field may be achieved by movingan instrument over the Earth's surface, for mineral, oil and gasexploration.

A gravimeter or gravity gradiometer may be used for detection ofmovement in the Earth's mantle and crust prior to earthquake or volcanicaction.

We claim:
 1. A proof mass support system comprising a pair of alignmentcoils for controlling the rest position of an elongate proof mass,wherein said alignment coils are constructed to provide a levitationforce when they carry electric currents which varies along the length ofsaid proof mass; and means for tuning the relative strength of saidelectric currents in said alignment coils to cause said proof mass totake up a predetermined orientation with respect to one or more degreesof freedom defined by said alignment coils.
 2. A system according toclaim 1 wherein said proof mass is formed of superconducting material,and said alignment coils are formed of superconducting material wherebysaid electric currents comprise persistent electric currents.
 3. Asystem according to claim 1 wherein at least one of said degrees offreedom comprises rotation about an axis substantially orthogonal to thedirection of said levitation force and to the length of said coils.
 4. Asystem according to claim 3 wherein said alignment coils comprisemeander-pattern coils.
 5. A system according to claim 1 wherein thedistance from one or both of said alignment coils to the surface of saidproof mass varies along the length of said alignment coil/s.
 6. A systemaccording to claim 5 further comprising a former having grooves in whichsaid alignment coils are wound, wherein the depth of said groovesincreases along said former's length.
 7. A system according to claim 1,wherein said alignment coils comprise interleaved sets of multiplewires.
 8. A system according to claim 1 wherein the number of turns perunit length of one or both of the coils varies along the length of thecoil/s.
 9. A system according to claim 8, wherein said alignment coilscomprise a pair of tapered, interleaved wires.
 10. A system according toclaim 1 wherein said proof mass is substantially cylindrical.
 11. Asystem according to claim 1 further comprising additional alignmentcoils adapted to provide levitation forces in other directions wherebylevitation of said proof mass against a gravitational field can beachieved in substantially all orientations of said proof mass withrespect to said gravitational field.
 12. A system according to claim 11,wherein at least two of said additional alignment coils comprise asecond pair of elongate coils which extend in substantially the samedirection as said first pair of alignment coils; and wherein said secondpair of alignment coils are constructed to provide a levitation forcewhen they carry electric currents which varies along the length of saidsecond pair of coils; said system further comprising means for tuningthe relative strength of said electric currents in said additionalalignment coils to cause said proof mass to take up a predeterminedorientation with respect to one or more degrees of freedom defined bysaid second pair of alignment coils.
 13. A system according to claim 1,wherein said alignment coils comprise Niobium wire wound on aninsulating former.
 14. A system according to claim 1 wherein said proofmass comprises a main body section with a ring extending therefrom. 15.A system according to claim 14, wherein a surface of said ring remotefrom said main body section is curved and a coil is located radiallyoutwardly of the surface of said ring such that a negative spring isformed.
 16. A system according to claim 1 further comprising a set ofconcave alignment coils which levitate said proof mass and produce anunstable equilibrium in use such that a negative spring is formed.
 17. Asystem according to claim 1, wherein said alignment coils extend alongthe length of said proof mass, and are constructed such that when theycarry electric currents they provide a levitation force which variesalong the length of said coils in a predetermined manner.
 18. A systemaccording to claim 1, wherein said pair of alignment coils are displacedwith respect to the center of mass of said proof mass along the lengthof said proof mass.
 19. An accelerometer comprising:an elongate proofmass having a sensitive axis and supported by a support system includinga pair of alignment coils for controlling the rest position of the proofmass, wherein said alignment coils are constructed to provide alevitation force when they carry electric currents which varies alongthe length of said proof mass, and the relative strength of saidelectric currents in sniff alignment coils is tuned to cause said proofmass to take up a predetermined orientation with respect to one or moredegrees of freedom defined by said alignment coils; and at least onesensing coil for monitoring movement of said proof mass due toacceleration of the proof mass with respect to the sensitive axis. 20.An accelerometer comprising:a first proof mass supported by a firstsupport system including a pair of first alignment coils for controllingthe rest position of the first proof mass, wherein said first alignmentcoils are constructed to provide a first levitation force when theycarry electric current which varies along the length of said first proofmass and the relative strength of said electric currents is tuned insaid first alignment coils to cause said first proof mass to take up acorresponding predetermined orientation; and a second proof masssupported by a second support system including a pair of secondalignment coils for controlling the rest position of the second proofmass, wherein said second alignment coils are constructed to provide asecond levitation force when they carry electric current which variesalong the length of said second proof mass and the relative strength ofsaid electric currents is tuned in said second alignment coils to causesaid second proof mass to take up a corresponding predeterminedorientation; wherein each proof mass has at least one associated sensingcoil for monitoring movement of each proof mass with respect to asensitive axis.
 21. An accelerometer according to claim 20, wherein saidalignment coils are arranged to orient said sensitive axis of each saidproof mass, further comprising means to tune the relative strength ofsaid currents in said alignment coils so as to align said sensitive axesof the proof masses with respect to each other in order to minimisealignment errors.
 22. An accelerometer according to claim 20, furthercomprising a differential-mode sensing circuit and a common-mode sensingcircuit connected to said sensing coils for sensing a change in thegravitational field strength wherein said common-mode sensing circuit issubstantially decoupled from said differential-mode circuit.
 23. Agravity gradiometer comprising:a first accelerometer including a firstproof mass and a pair of first alignment coils for controlling the restposition of the first proof mass and wherein said first alignment coilsprovide a levitation force which varies along the length of said firstproof mass and the relative strength of said electric currents is tunedin said first alignment coils to cause said first proof mass to take upa corresponding predetermined orientation; and a second accelerometerincluding a second proof mass and a pair of second alignment coils forcontrolling the rest position of the second proof mass, wherein saidsecond alignment coils provide a levitation force which varies along thelength of said second proof mass and the relative strength of saidelectric currents is tuned in said second alignment coils to cause saidsecond proof mass to take up a corresponding predetermined orientation.24. A gradiometer according to claim 23, further comprising adifferential-mode sensing circuit and a common-mode sensing circuitconnected to said sensing coils for sensing a change in thegravitational field strength wherein said common-mode sensing circuit issubstantially decoupled from said differential-mode circuit.
 25. Agravity gradiometer according to claim 23, wherein said alignment coilsare arranged to orient said sensitive axis of each said proof mass,further comprising means to tune the relative strength of said currentsin said alignment coils so as to align said sensitive axes of the proofmasses with respect to each other in order to minimize alignment errors.